where \(\lambda \)  is some penalty function that may only appear when certain circuit structures appear, as well as other kinds of penalty terms, like penalty on the sum of absolute value of weights or the number of certain type of gates in the circuit; \(L\)  and \(R\)  are the loss/reward before applying the penalty. The purpose of the penalty term \(\lambda \)  is to `sway' the search algorithm from structures we do not desire.
Instead of storing all the operation parameters for each different quantum circuit, we share the parameters for a single operation at a certain location. That is, we have a multidimensional array of shape \((p, c, l)\) , where \(l\)  is the maximum number of parameters for the operations in the operation pool. If all the operations in the pool are just the \(U3\)  gate [1]}:
\(U 3(\theta , \phi , \lambda )=\left[\begin{array}{cc}\cos \left(\frac{\theta }{2}\right) & -e^{i \lambda } \sin \left(\frac{\theta }{2}\right) \\e^{i \phi } \sin \left(\frac{\theta }{2}\right) & e^{i(\phi +\lambda )} \cos \left(\frac{\theta }{2}\right)\end{array}\right]\) 
